n 1997, an experiment at the Camp Blanding center for lightning testing [1] challenged the predominant view that ground rods are essentially resistive. What that experiment found was that the waveshapes of lightning currents in a building grounding system and those entering the electrical circuits of the building were considerably different. That was at odds with IEC 61312-1:1995 [2] assertions that they should be the same. The conclusion was that, for lightning, the ground rod had an impedance with a reactive component in addition to the resistive one.
So how do we take into account the impedance effects for lightning? Well, it turns out not to be so simple. Professor Leonid Grcev, who with his students has conducted extensive studies of grounds, has found that a simple modeling of a ground rod as an R-L-C circuit doesn’t give correct results, due to surge propagation effects which cause a deviation from the low frequency behavior during the fast-transient period. So the challenge is to determine what this deviation is.
Considering normal grounds (those not chemically treated or otherwise enhanced), Grcev has shown that they can be characterized in terms of effective length and impulse coefficient (IC) [3]. The IC is the ratio of peak voltage across an actual ground rod to the peak voltage across a purely resistive ground rod in response to a surge. It shows how the impedance of the ground rod affects the expected peak voltage due to a surge relative to what it would have been if the ground rod were purely resistive.
The first thing to consider is the ground rod effective length leff, which is the maximum length of the ground electrode for which the impulse coefficient is equal to one. leff will be used later in the discussion of the IC (which is what we really want).
where:
where A = Z/R is the impulse coefficient, Z is the effective impedance, R is the ground rod resistance, α is calculated from equation (2), and β is calculated from equation (3).
For A > 1, the ground rod has an effective series inductance in addition to its resistance. In this case, the peak voltage will be A times bigger than it would have been if the ground rod were purely resistive.
For A < 1, the ground rod has an effective parallel capacitance in addition to its resistance. In this case, the peak voltage will be A times lower than it would have been if the ground rod were purely resistive.
From equation (4) the effect of the ground rod reactance can be calculated. As an illustration, take the four cases of ρT1, = 100, 300, 1000, and 10,000, and use equation (4) to plot the impulse coefficient A vs. length of the rod. Ground rods with a low ρT1 product have a high impulse coefficient, whereas ground rods with a high ρT1 product have a low impulse coefficient, as shown in Figure 2.
Figure 3 is a replot of Figure 2 for ground rods of a length normally used (≤ 10 m).
To calculate Irod we need to calculate the fraction of the lightning current Imax captured by the ground rod. IEEE Std 142 [5] shows that 99% of the current flowing in the ground rod is captured in a volume having a radius of twice a ground rod length, s. Figure 4 illustrates this situation, where d is the distance from the lightning strike point to the edge of a cylinder representing the ground rod outer effective extent.
Note that the arcsin is not defined for arguments greater than 1, so there are two cases for equation (6): Case 1 where d ranges from 2s to infinity, and case 2 where d ranges from 2s to 0.
For case 1, if the arcsin is in degrees, then the fraction f1 of the lightning current Imax captured by the ground rod is:
The peak voltage is calculated from equation (5). The effective impedance Z of the ground rod to be used in equation (5) can be calculated from Dwight’s [4] equation multiplied by A:
Substituting equations (9) and (10) in equation (5):
For these cases, Figure 5 shows how Vpeak changes due to a decrease in ground-rod current capture with increasing distance.
Applicability of the Peak Voltage Calculation
With the foregoing discussions in mind, different lightning waveforms, different ρ, and different ground rod lengths will result in different peak voltages from those shown in Figure 5.
The usual assumption that ground rods are purely resistive is actually not what is observed in the case of lightning. Particularly for the relatively short ground rods commonly used, during the rise-time period the ground rods look like an impedance with a significant capacitive component. The result is that for these commonly used ground rods, the peak voltage due to a lightning strike is generally significantly lower than would be the case for a purely resistive ground rod. Whether the peak voltage is higher or lower than for a purely resistive ground rod depends on a number of variables, including the surge waveform, the ground resistivity, the length of the ground rod, and the distance the observer is from the lightning strike point. The peak voltage across the ground rod can be calculated, based on estimates of these variables.
- V. A. Rakov et al, “Direct Lightning Strikes to the Lightning Protective System of a Residential Building: Triggered-lightning Experiments,” IEEE Transactions on Power Delivery, vol. 17, no. 2 (April 2002).
- IEC Standard 61312-1:1995, Protection Against Lightning Electromagnetic Impulse- Part 1: General Principles.
- L. Grcev, “Impulse Efficiency of Ground Rods,” IEEE Transactions on Power Delivery, vol. 24, no. 1 (January 2009), 441-451.
- H. B. Dwight, “Calculation of Resistances to Ground,” Transactions of the American Institute of Electrical Engineers, vol. 55 (1936), 1319-1328.
- IEEE Std 142-1991, IEEE Recommended Practice for Grounding of Industrial and Commercial Power Systems.
- MIL-HDBK-419, Military Handbook Grounding, Bonding, and Shielding for Electronic Equipments and Facilities, Volume 1 of 2 Volumes on Basic Theory, January 1982.
- Cigre TB549, Lightning Parameters for Engineering Applications, August 2013.
- A. Geri, “Behaviour of Grounding Systems Excited by High Impulse Currents: The Model and Its Validation,” IEEE Transactions on Power Delivery, vol. 14, no. 3, July 1999.
- L. Grcev and V. Arnautovski, Proceedings of 24th International Conference on Lightning Protection (ICLP’98), Birmingham, UK, 14-18 September 1998, vol. 1, pp. 524-529